The aim of this project is to obtain a detailed image of macromolecular complexes of tRNA with tRNA synthetases, and similar functional complexes of proteins and nucleic acids. The compelling biological interest of these complexes arises from their central role in protein biosynthesis. We will improve the image quality, refine and extend the phases of the X-ray diffraction pattern of the complex of tRNA-Asp-Aspartyl-tRNA-Synthetase from yeast, orthorhombic form, at 4.0 A resolution, starting from an image obtained from the cubic form of the same complex at 10.0 A resolution. We will extend this procedure to other problems, such as the complex of tRNA f MEt-f MET synthetase and the Tryptophan-repressor DNA complex. New methods to replace or supplement MIR phasing methods will be developed. These methods will be based on known properties of the electron density, like positivity, maximum value, continuity, solvent flatness, atomicity, and non-crystallographic symmetry. Measures of minimum bias (or maximum "entropy") will be introduced. A comprehensive algorithm based on Fast Fourier Transforms will be constructed and applied to the above mentioned cases.